# Thermal Efficiency Calculator

URL: https://speedycalculator.com/calculators/physics/thermal-efficiency/
Last updated: 2026-10-30

> The thermal efficiency calculator finds the efficiency of a heat engine from its heat input and work output (or heat rejected), and compares it with the reversible (Carnot) limit for given temperatures.

## Inputs

- Engine
- Heat input Q_in (J, kJ, MJ, kWh, cal, kcal, BTU)
- Work output W (J, kJ, MJ, kWh, cal, kcal, BTU)
- Heat rejected Q_out (J, kJ, MJ, kWh, cal, kcal, BTU)
- Hot temperature (°C, °F, K)
- Cold temperature (°C, °F, K)

## Results

- Thermal efficiency

## Formula

```
η = W/Q_in = 1 − Q_out/Q_in · Reversible: η_max = 1 − T_c/T_h
```

## Explanation

Thermal efficiency measures how much of the heat burned in an engine becomes useful work. Car engines manage 25–40%, modern combined-cycle power plants over 60%.

### How to use the Thermal Efficiency Calculator

- **Engine**
- **Heat input Q_in**
- **Work output W**
- **Heat rejected Q_out**
- **Hot temperature**
- **Cold temperature**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose irreversible (real data) or reversible (temperatures) and enter the values.

### Tips

- Use absolute temperature (K) in gas laws and efficiency formulas.
- Temperature differences are the same in K and °C.
- Heat = mass × specific heat × temperature change when no phase change occurs.
- Phase changes need latent heat at a constant temperature.

### Common mistakes to avoid

- Using °C in pV = nRT.
- Forgetting latent heat during melting or boiling.
- Confusing heat capacity (J/K) with specific heat (J/(kg·K)).

### Inputs explained

FieldWhat to enterEngineChoose one: Real engine – heat and work, Real engine – heat in and out, Reversible (Carnot)Heat input Q_inUnits: J, kJ, MJ, kWh, cal, kcal …Work output WUnits: J, kJ, MJ, kWh, cal, kcal …Heat rejected Q_outUnits: J, kJ, MJ, kWh, cal, kcal …Hot temperatureUnits: °C, °F, KCold temperatureUnits: °C, °F, K

### Example values

How the main result changes when **Heat input Q_in** changes and everything else stays at the example values above:

Heat input Q_in (J)Thermal efficiency (%)50707546.6667100351252815023.333320017.5

## Worked example

Inputs — Engine: Real engine – heat and work; Heat input Q_in: 100 J; Work output W: 35 J.

Results — **Thermal efficiency = 35 %**.

## Key terms

- **Heat engine**: Device converting heat into work.

## FAQ

**Why is thermal efficiency always below 100%?**
The second law of thermodynamics requires heat rejection.

**What is a typical car engine efficiency?**
About 25–35% in normal driving.

**How do combined-cycle plants reach 60%?**
Exhaust heat from a gas turbine drives a steam turbine.

**What limits the efficiency?**
The temperatures available and irreversibilities.

**What formula does the Thermal Efficiency Calculator use?**
η = W/Q_in = 1 − Q_out/Q_in · Reversible: η_max = 1 − T_c/T_h.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)